What is the Greatest Common Factor of 10129 and 10140?

Greatest common factor (GCF) of 10129 and 10140 is 1.

GCF(10129,10140) = 1

We will now calculate the prime factors of 10129 and 10140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10129 and 10140.

How to find the GCF of 10129 and 10140?

We will first find the prime factorization of 10129 and 10140. After we will calculate the factors of 10129 and 10140 and find the biggest common factor number .

Step-1: Prime Factorization of 10129

Prime factors of 10129 are 7, 1447. Prime factorization of 10129 in exponential form is:

10129 = 7¹ × 1447¹

Step-2: Prime Factorization of 10140

Prime factors of 10140 are 2, 3, 5, 13. Prime factorization of 10140 in exponential form is:

10140 = 2² × 3¹ × 5¹ × 13²

Step-3: Factors of 10129

List of positive integer factors of 10129 that divides 10129 without a remainder.

1, 7, 1447

Step-4: Factors of 10140

List of positive integer factors of 10140 that divides 10129 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 169, 195, 260, 338, 390, 507, 676, 780, 845, 1014, 1690, 2028, 2535, 3380, 5070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10129 and 10140. The biggest common factor number is the GCF number.
So the greatest common factor 10129 and 10140 is 1.

Also check out the Least Common Multiple of 10129 and 10140